Cylindrical polarimetric phased array radar
Summary by NHIP
Cylindrical polarimetric radar
The method directs signals to a cylindrical panel array to transmit a dual H and V polarized beam with uniform azimuth width and maintained cross-polarization isolation. Selected panels receive scattered reflection signals possessing a specific frequency spectrum for processing into electronic radar output.
Claim Score by NHIP
Abstract
A method of collecting data using a polarimetric phased array antenna is described. The method includes directing electromagnetic signals to selected panels of an array of panels so as to transmit a dual H and V polarized electromagnetic beam (1) having the same beam width in all azimuth directions and (2) maintaining cross-polarization isolation via orthogonal dual-polarizations in all beam pointing directions. The panels include antennas having a horizontally (H) polarized array element and a vertically (V) polarized array element arranged to form two orthogonally polarized horizontal and vertical radiating fields which together form the dual H and V polarized electromagnetic beam. The array of panels is arranged so as to form a substantially cylindrical configuration on a support system. Reflection signals sensed by the selected panels formed by scattering of said dual H and V polarized electromagnetic beam are received and have a reflection frequency spectrum.
Term
Projected expiry 12 May 2031.
- Priority
- Filed
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- Projected expiry
22 claims: 3 independent, 19 dependent
- 1Broadest claimClaim Score 34, narrow(NHIP)A method of collecting data using a polarimetric phased array antenna, the method comprising:directing electromagnetic signals to one or more selected panels of an array of panels so as to transmit and commutating scan a dual H and V polarized electromagnetic beam, wherein said dual H and V polarized electromagnetic beam (1) has the same beam width in all azimuth directions and (2) maintains cross-polarization isolation via orthogonal dual-polarizations in all beam pointing directions, the array of panels comprising a plurality of antennas, wherein each antenna comprises a horizontally (H) polarized array element and a vertically (V) polarized array element arranged to form two orthogonally polarized horizontal and vertical radiating fields which together form the dual H and V polarized electromagnetic beam, wherein the array of panels is arranged so as to form a substantially cylindrical configuration on a support system;and receiving reflection signals sensed by the one or more selected panels formed by scattering of said dual H and V polarized electromagnetic beam, wherein said reflection signals have a reflection frequency spectrum configured to be processed into an electronic radar output.
- 8A method of collecting data using a polarimetric phased array antenna, the method comprising:forming electromagnetic signals based on a phase shift term and a weighting matrix;directing the electromagnetic signals to one or more selected panels of an array of panels so as to transmit and commutating scan a dual H and V polarized electromagnetic beam, wherein said dual H and V electromagnetic beam (1) has the same beam width in all azimuth directions and (2) maintains cross-polarization isolation via orthogonal dual-polarizations in all beam pointing directions, the array of panels comprising a plurality of antennas, wherein each antenna comprises a horizontally (H) polarized array element and a vertically (V) polarized array element arranged to form two orthogonally polarized horizontal and vertical radiating fields which together form the dual H and V polarized electromagnetic beam, wherein the array of panels is arranged so as to form a substantially cylindrical configuration on a support system;and receiving reflection signals sensed by the one or more selected panels formed by scattering of said dual H and V polarized electromagnetic beam, wherein said reflection signals have a reflection frequency spectrum configured to be processed into an electrical radar output.
- 15A method of collecting data using a polarimetric phased array antenna, the method comprising:forming at least one first electromagnetic signal based on a first phase shift term and a first weighting matrix;forming at least one second electromagnetic signal based on a second phase shift term and a second weighting matrix;directing the at least one first electromagnetic signal to one or more selected first panels of an array of panels so as to transmit and commutating scan at least one first dual H and V polarized electromagnetic beam, wherein said at least one first dual H and V polarized electromagnetic beam (1) has the same beam width in all azimuth directions and (2) maintains cross-polarization isolation via orthogonal dual-polarizations in all beam pointing directions, the array of panels comprising a plurality of antennas, wherein each antenna comprises a horizontally (H) polarized array element and a vertically (V) polarized array element arranged to form two orthogonally polarized horizontal and vertical radiating fields which together form the dual H and V polarized electromagnetic beam, wherein the array of panels is arranged so as to form a substantially cylindrical configuration on a support system;directing the at least one second electromagnetic signal to one or more selected second panels of the array of panels so as to transmit and commutating scan at least one second dual H and V polarized electromagnetic beam, wherein said at least one second dual H and V polarized electromagnetic beam (1) has the same beam width in all azimuth directions and (2) maintains cross-polarization isolation via orthogonal dual-polarizations in all beam pointing directions;and receiving reflection signals sensed by the one or more first or second selected panels formed by scattering of said at least one first and second dual H and V polarized electromagnetic beams, wherein said reflection signals have a reflection frequency spectrum configured to be processed into an electronic radar output.
Independent claims3
77 paragraphs in 7 sections, as filed
INCORPORATION BY REFERENCE/CROSS-REFERENCE TO RELATED APPLICATIONS
0001The present patent application is a continuation patent application of the patent application identified by U.S. Ser. No. 12/947,523, filed on Nov. 16, 2010, now U.S. Pat. No. 8,988,274, which claims priority to the United States Provisional Patent Application identified by U.S. Ser. No. 61/261,695 which was filed on Nov. 16, 2009; the entire contents of both applications are hereby incorporated herein by reference.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
0002This invention was made with government support under contract number ATM 0608168 awarded by the National Science Foundation; and contract number NA 080AR4320886 awarded by the National Oceanic and Atmospheric Administration. The government has certain rights in the invention.
THE NAMES OF THE PARTIES TO A JOINT RESEARCH AGREEMENT
0003Not Applicable.
REFERENCE TO A “SEQUENCE LISTING,” A TABLE, OR A COMPUTER PROGRAM LISTING APPENDIX SUBMITTED ON A COMPACT DISC AND AN INCORPORATION-BY-REFERENCE OF THE MATERIAL ON THE COMPACT DISC
0004Not Applicable.
BACKGROUND
0005It is becoming widely accepted that radar polarimetry provides accurate and informative weather measurements, while phased array radar (PAR) technology can shorten data update time. This suggests that the future weather radar should have the functions of both polarimetry and electronic steering capabilities, i.e., Polarimetric Phased Array Radar (PPAR), allowing multi-missions of weather surveillance and target detection.
0006In addition to military applications for target recognition and tracking (Brookner 2007), Phased Array Radar (PAR) technology has recently been successfully introduced to the weather community. A phased array weather radar, the National Weather Radar Testbed (NWRT) operating at a wavelength of 9.38 cm, was developed in Norman, Okla. through a joint effort of a government/university/industry team (Zrnic et al. 2007). The NWRT demonstrated that its pulse-to-pulse electronic beam steering capability enables as accurate meteorological measurements in shorter storm surveillance times as achieved with a conventional dish antenna having a mechanically steered beam. The shorter surveillance times result in faster data updates and the capability to observe detailed evolutions of severe storm phenomena (Yu et al. 2007; Heinselman et al. 2008). The NWRT also has a hybrid capability to both mechanically and electronically steer the beam. This capability has allowed multi-pattern measurements of the same meteorological volume to successfully mitigate both stationary and moving clutter (Zhang et al. 2010). Furthermore, the NWRT uses an antenna from the AN/SPY1-A monopulse radar of the Aegis system (Sherman, 1988), which has sum and difference channels; these can be combined to implement Spaced Antenna Interferometry (SAI) techniques for crossbeam wind measurement (Zhang and Doviak 2007), and sub-volume inhomogeneity/object detection (Zhang and Doviak 2008). It has been also theorized that the AN/SPY1-A auxiliary channels could support implementation of adaptive clutter cancellation techniques (Le et al. 2009).
0007While PAR technology has recently received wide-spread attention in the weather community, weather radar polarimetry has matured to a point that it is being implemented on the national network of WSR-88D Doppler radars (Doviak et al. 2000) using its conventional dish antenna. Polarimetric radar provides multi-parameter measurements that reveal detailed microphysics of storms in addition to hydrometeor classification, accurate precipitation estimation and improved weather nowcasts. Therefore, the weather community and the nation expect that the future Multi-function Phased Array Radar (MPAR) will retain all the capabilities of the polarimetric WSR-88D (Smith et al. 2008). It is the polarimetric capability which the 2nd MPAR symposium (http://www.ofcm.noaa.gov/mpar-symposium, 17-19 Nov. 2009, Norman, Okla.) identified as the most challenging technical issue that the community is facing. The challenge comes from the fact that highly accurate polarimetric radar measurements are required to provide meaningful information. But biases inherent to Planar Polarimetric Phased Array Radar (PPPAR) exist and can be larger than the intrinsic values if the beam is directed away from the planar array's broadside. For example, the intrinsic ZDR values range only from about 0.1 dB for drizzle and dry snow to 3-4 dB for heavy rain and large drops. Thus, it is desirable that the measurement error for ZDR be of the order of 0.1 dB (Zhang et al. 2001, Brandes et al. 2003). But the ZDR bias for a PPPAR can be a few dBs (Zhang et al. 2009a). Hence, it is crucial for the success of the MPAR project that the system configuration for a PPPAR is selected correctly and designed optimally.
0008In the presentation at the 34th AMS radar conference, a number of issues with PPAR for weather measurements have been listed and discussed, including sensitivity, bias, calibration, cross-polar isolation, array configuration, polarization mode selection, waveform optimization, and signal processing and display. The polarization bias was quantified and a calibration procedure was proposed by Zhang et al. (2009) for planar arrays. The other issues remain.
0009As background, a variety of antenna array configurations exist including linear array, planar array, circular/cylindrical array, and spherical array. The linear array needs one mechanical rotation for weather surveillance like the rapid Doppler On Wheels (rapid DOW) (Wurman 2003) and the proposed design for CASA (Hopf et al. 2009). For the planar array, multiple faces (normally four) are needed (e.g., the SPY-1A). But the planar array has sensitivity loss and polarization bias if the beam points away from the broadside (Zhang et al. 2009a). Antennas having circular or cylindrical configurations have been used for direction finding and communications (Royer 1966; Raffaelli and Johansson 2003) but not with a dual-polarization phased-array radar, (multi-function or single function), for weather related tasks. For satellite communication applications, the spherical array is optimal and flexible in its use of the antenna aperture size and in its symmetry (Tomasic et al. 2002).
0010With respect to PPAR, possible antenna array configurations for PPAR include linear array, 2D planar array, and spherical array. The linear array needs one mechanical rotation for weather surveillance like rapid DOW (Wurman, 2003) and the proposed design for CASA (Hopf et al. 2009). For planar array, multiple faces (normally four) are needed (e.g., the SPY-1A or, as with the NWRT a composite of mechanical and electronic beam steering. The planar array has issues of sensitivity loss and polarization bias when the beam points away from the broadside (Zhang et al. 2009). A spherical array is optimal and flexible in terms of using the antenna aperture and has the symmetry in all the directions (Tomasic et al. 2002) needed for receiving signals from satellites. For weather applications, however, the spherical array can have problems in making polarimetric measurement of weather because high cross-polar isolation is required.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING
Implementations of the invention may be better understood when consideration is given to the following detailed description thereof. Such description makes reference to the annexed pictorial illustrations, schematics, graphs, drawings, and appendices. In the drawings:
<figref idref="DRAWINGS">FIG. 1</figref> is a schematic diagram of a radar data acquisition system constructed in accordance with one version of the present invention.
<figref idref="DRAWINGS">FIG. 2<i>a </i></figref>is a perspective view of a polarimetric phased array antenna constructed in accordance with a version of the present invention.
<figref idref="DRAWINGS">FIG. 2<i>b </i></figref>is a perspective view of a version of the polarimetric phased array antenna.
<figref idref="DRAWINGS">FIG. 3</figref> is a schematic diagram of four dual polarization electromagnetic beams being simultaneously emitted by the polarimetric phased array antenna.
<figref idref="DRAWINGS">FIGS. 4<i>a </i>and 4<i>b </i></figref>are side elevational views of exemplary panels of the polarimetric phased array antenna having a dual-polarization capability with either a single element (<figref idref="DRAWINGS">FIG. 4<i>a</i></figref>) or interlaced cross polar radiating rectangular apertures/patches (<figref idref="DRAWINGS">FIG. 4<i>b</i></figref>) that preferably have proven low cross polar radiation.
<figref idref="DRAWINGS">FIG. 5</figref> is a schematic view of a switching network establishing communication between multiple panels of the polarimetric phased array antenna and one or more transmitter and receiver of the radar control and processing system.
<figref idref="DRAWINGS">FIG. 6</figref> is a diagram showing a coordinate system for the polarimetric phased array antenna constructed in accordance with the present invention.
<figref idref="DRAWINGS">FIG. 7</figref> is a table of exemplary designs for a polarimetric phased array antenna with two, three or four dual polarization electromagnetic beams being simultaneously emitted by the polarimetric phased array antenna.
<figref idref="DRAWINGS">FIGS. 8(<i>a</i>) and 8(<i>b</i>)</figref> are graphs showing copolar and cross-polar one-way power density patterns as a function of azimuth and zenith angle
<figref idref="DRAWINGS">FIGS. 9(<i>a</i>), 9(<i>b</i>), 9(<i>c</i>) and 9(<i>d</i>)</figref> are simulated one-way power density patterns for a four-beam configuration and element spacing of 0.5λ without tapering, density adjustment, or polarization compensation.
<figref idref="DRAWINGS">FIGS. 10(<i>a</i>), 10(<i>b</i>), 10(<i>c</i>) and 10(<i>d</i>)</figref> are simulated one-way power density patterns for the four-beam configuration and element spacing of 0.5λ with tapering, but without density adjustment, or polarization compensation.
<figref idref="DRAWINGS">FIGS. 11(<i>a</i>), 11(<i>b</i>), 11(<i>c</i>) and 11(<i>d</i>)</figref> are simulated one-way power density patterns for the four-beam configuration and element spacing of 0.5λ with tapering, element density correction and polarization compensation.
DETAILED DESCRIPTION
0024Numerous applications of the present invention are described, and in the following description, numerous specific details are set forth. However, it is understood that implementations of the invention may be practiced without these specific details. Furthermore, while particularly described with reference to weather radars, aspects of the invention are not so limited. For example, the polarimetric phased array radar disclosed below is applicable to the passive reception of data, the transmission of data and combinations thereof in communications and remote sensing. Further, the polarimetric phased array radar can be used for automatic target detection and recognition in military and civilian applications.
0025Referring now to the drawings, and in particular to <figref idref="DRAWINGS">FIG. 1</figref>, shown therein and designated by reference numeral <b>10</b> is a radar data acquisition system constructed in accordance with the present invention. In general, the radar data acquisition system <b>10</b> is provided with a polarimetric phased array antenna <b>12</b>, and a radar control and processing system <b>14</b>. The polarimetric phased array antenna <b>12</b> can include a cylindrical arrangement for orthogonal dual-polarizations and the same beam-width in all azimuth directions. In general, the polarimetric phased array antenna <b>12</b> is provided with a support system <b>18</b>, an array of panels <b>20</b>, and a switching network <b>22</b>. The polarimetric phased array antenna <b>12</b> can also optionally be provided with a cover (also known as a radome) <b>24</b>. Much of the electronic systems can be housed inside the support system <b>18</b>, if desired.
0026The support system <b>18</b> can be constructed in any suitable manner, such as one or more inflatable device, or one or more interconnected system of brackets, and/or flanges and/or other mechanical supports such as bolts, fasteners, welds, or the like. The support system <b>18</b> can either be stationary or mounted to a movable pedestal. The support system <b>18</b> can be connected to a ground station, a building, a communication tower, a ship, a ground based vehicle, and/or a manned or unmanned airplane, airborne vehicle or the like.
0027The array of panels <b>20</b> are supported by the support system <b>18</b> in a substantially cylindrical configuration. That is, the panels <b>20</b> can include a planar configuration, and in one embodiment the panels <b>20</b> have a same size, i.e., width and/or height. In one embodiment, the support system <b>18</b> supports the panels <b>20</b> at a non-zero angle relative to the horizontally adjacent panels <b>20</b>, and in the same plane as the vertically adjacent panels <b>20</b> such that the panels <b>20</b> surround the support system <b>18</b> to form the substantially cylindrical configuration. The number of panels and/or facets in the polarimetric phased array antenna <b>12</b> can be varied depending upon the desired use of the polarimetric phased array antenna <b>12</b>. Further, while the panels <b>20</b> are depicted in a square configuration, it should be understood that the shape of the panels <b>20</b> can also be varied. For example, the panels <b>20</b> can be provided with any symmetric, asymmetric or other geometries, such as square, rectangular, triangular, circular, or the like. In one aspect, the shape of the panels <b>20</b> is chosen such that the panels <b>20</b> can be aligned at their edges to form the array.
0028The switching network <b>22</b> communicates with the panels <b>20</b> such that at least one of power, radar and control signals are sent to and received from one or more selected panels <b>20</b>. One or more (and in one embodiment all) of the plurality of the panels <b>20</b> include a dual polarization antenna <b>26</b> (see the plus signs in <figref idref="DRAWINGS">FIG. 2</figref>, and <figref idref="DRAWINGS">FIG. 4<i>a</i></figref>) as well as other elements that are not shown and would be known by one skilled in the art for forming, steering and/or receiving at least one single and/or dual polarization electromagnetic beam having preselected characteristics, such as a communication network, buffers or the like.
0029Panels <b>20</b> can also or in the alternative include a single polarization antenna, for example. For example, the panels <b>20</b> can include interlaced single polarized radiating elements <b>29</b><i>a </i>and <b>29</b><i>b </i>arranged in an interlaced fashion as shown in <figref idref="DRAWINGS">FIG. 4<i>b </i></figref>to form two orthogonally polarized radiating fields. The dual polarization antenna <b>26</b> will be discussed herein by way of example. The dual polarization antenna <b>26</b> can be referred to herein as “dual polarization antenna element”. The dual polarization antenna element <b>26</b> is formed using any suitable hardware, such as a patch antenna configuration (e.g., having a single element with two different antenna areas for forming the dual polarization electromagnetic beam), a dipole antenna configuration, or a pair of dipoles <b>28</b><i>a </i>and <b>28</b><i>b</i>. The pair of dipoles <b>28</b><i>a </i>and <b>28</b><i>b </i>can be constructed of conductive element(s) arranged in a cross-pattern. The dual polarization antenna element <b>26</b> can also be formed of either dipoles and/or aperture(s) and/or a patch.
0030The radar control and processing system <b>14</b> is provided with a variety of equipment that is used to form the electromagnetic signals which are directed to one or more of the selected panels <b>20</b> (e.g., independent panels or groups of panels) such that the selected panels <b>20</b> form single or dual polarization electromagnetic beams. When two or more panels <b>20</b> are selected, such selected panels <b>20</b> cooperate to form the dual polarization electromagnetic beam. The radar control and processing system <b>14</b> is also provided with equipment for reading signals sensed at r<sub>mn</sub>=a<sub>x</sub>R cos φ<sub>n</sub>+a<sub>y</sub>R sin φ<sub>n</sub>+a<sub>z</sub>z<sub>m </sub>on one or more selected panels <b>20</b> (e.g., independent panels or groups of panels) and for decoding the signals into an electronic radar output.
0031In general, the radar control and processing system <b>14</b> can be provided with one or more transmitters <b>30</b>, one or more receivers (two being shown by way of example as <b>32</b><i>a </i>and <b>32</b><i>b</i>), one or more communication servers <b>34</b>, one or more digital signal processors <b>36</b>, one or more synchronizers <b>38</b>, one or more RF sources <b>40</b>, one or more data acquisition units <b>42</b>, one or more host computer <b>44</b>, and one or more user/maintenance workstation <b>46</b> communicating with each other, as shown for example, in <figref idref="DRAWINGS">FIG. 1</figref>. The radar control and processing system <b>14</b> can be constructed in a variety of manners using a combination of one or more hardware and one or more software elements. For example, a discussion of suitable hardware and/or software elements forming the elements of the radar control and processing system <b>14</b> is described in Exhibit A of the provisional patent application identified by U.S. Ser. No. 61/261,695, with the exception that such hardware and/or software elements, such as the synchronizer depicted in <figref idref="DRAWINGS">FIG. 1</figref> and described on page 259 can be modified to cause the transmitter(s) and/or receivers(s) to communicate with (e.g., send and receive signals) particular one(s) of the panels <b>20</b> at known location(s) or pointing in known direction(s). For example, the synchronizer <b>38</b> can have access to (or be programmed with) addresses specifically identifying the panels <b>20</b>, data indicative of the location(s) of the panel(s) <b>20</b>, and/or data indicative of the direction in which the panel(s) are facing, and then digital or analog commands generated by the synchronizer <b>38</b> can include the address of the particular panel(s) <b>20</b> to send and/or receive signals from one or more selected panel <b>20</b>.
0032The synchronizer <b>38</b> of the radar control and processing system <b>14</b> can use any suitable protocol or control sequence for driving the panel(s) <b>20</b> of the polarimetric phased array antenna <b>12</b>. For example, suitable protocols referred to as “simultaneous transmitting and simultaneous receiving (STSR) mode” and “alternating transmitting but simultaneous receiving (ATSR)” are described in Exhibit B of the provisional patent application identified by U.S. Ser. No. 61/261,695. As would be understood by one skilled in the art, some of the components within the radar control and processing system <b>14</b> are optional, such as the one or more communication servers <b>34</b>, one or more digital signal processors <b>36</b>, one or more synchronizers <b>38</b>, one or more data acquisition units <b>42</b>, and one or more host computer <b>44</b>.
0033When the support system <b>18</b> includes a movable pedestal, the radar control and processing system <b>14</b> can also include an antenna pedestal control as discussed in Exhibit A of the provisional patent application identified by U.S. Ser. No. 61/261,695.
0034In various aspects, the radar data acquisition system <b>10</b> includes a variety of advantages, such as the allowance of simultaneous multi-beams <b>50</b><i>a</i>-<i>d </i>(<figref idref="DRAWINGS">FIG. 3</figref>) to utilize the polarimetric phased array antenna <b>12</b> for data acquisition while maintaining high-quality polarimetric data. For example, in one embodiment, the polarimetric phased array antenna <b>12</b> can have a measurement error for the differential reflectivity within 0.2 dB and for copolar cross-correlation coefficient within 0.02; the simultaneous use of multiple beams <b>50</b><i>a</i>-<i>d</i>, for example, emitted from and/or received by the polarimetric phased array antenna <b>12</b>; and the maintenance of cross-polarization isolation. In particular, the polarimetric phased array antenna <b>12</b>, by way of example, can allow simultaneous (or alternating) multi-beams <b>50</b><i>a</i>-<i>d </i>to utilize the antenna resource for data update while maintaining high-quality polarimetric data.
0035The number of simultaneous or alternating beams may be chosen to be 2, 3, 4, or the like and in one aspect of the invention provides radar coverage of 360 degrees around the polarimetric phased array antenna <b>12</b> with electronic steering and/or scanning of the beam(s) <b>50</b> in the horizontal and vertical directions. When four beams <b>50</b><i>a</i>-<i>d </i>are transmitted and/or received, the polarimetric phased array antenna <b>12</b> functions similarly to a SPY-1A radar having four antenna faces with each antenna face providing coverage of approximately 90 degrees. But, the polarimetric phased array antenna <b>12</b> can maintain the same beam width and polarization characteristics with axial symmetry. When the polarimetric phased array antenna <b>12</b> is used to simultaneously transmit only two beams <b>50</b> (not shown), such beams <b>50</b> can be transmitted in the back to back directions and a maximal aperture can be used so that the finest resolution desired can be achieved. It should be noted that the synchronizer <b>38</b> can be programmed to vary the size of the aperture and/or the resolution. By considering the trade-off between the resolution and update time, three beams may be an adequate choice, as the antenna aperture for each beam can be reduced only 13% from the maximum.
0036The radar data acquisition system <b>10</b> having the polarimetric phased array antenna <b>12</b> can be used for practically scan-invariant weather measurements. In this regard, the polarimetric phased array antenna <b>12</b> has azimuth scan-invariant properties and has very minor dependence on elevation at low elevation angles. Because the WSR-88D scan strategy has coarser elevation sampling at higher elevation angles, and because the angular resolution of the polarimetric phased array antenna <b>12</b> coarsens as beam elevation angle increases (thus filling angular gaps created by coarser sampling), the gradual decrease in elevation resolution is a beneficial feature.
0037Referring again to <figref idref="DRAWINGS">FIG. 2<i>b</i></figref>, there may be M×N dual polarization antennas <b>26</b> arranged azimuthally (M) and axially (N) on panels <b>26</b> forming an outer surface <b>100</b> of a cylinder <b>102</b>. Multiple simultaneous beams <b>50</b> can be formed with each beam <b>50</b> generated from a sector (or panel <b>20</b>) of the outer surface <b>100</b> with a broadside direction, i.e., front looking direction, along a center, i.e., bisector, of the illuminated sector. A sector is defined as a collection of contiguous panels <b>20</b> that work together to create the beam <b>50</b>. For example, if four beams <b>50</b> will be generated by the the polarimetric phased array antenna <b>12</b>, then four 90 degree sectors can be defined and all of the panels <b>20</b> within a particular sector can be used to form the beam <b>50</b>. The beam <b>50</b> is preferably emitted from a center of the sector. Using a cylindrical configuration for the polarimetric phased array antenna <b>12</b>, polarization orthogonality is preserved in all directions.
0038Referring now to <figref idref="DRAWINGS">FIG. 6</figref>, shown therein is an exemplary coordinate system <b>110</b> which will be used to describe the radiation characteristics of the cylindrical configuration for the polarimetric phased array antenna <b>12</b> utilized by the radar control and processing system <b>14</b> for forming the electromagnetic signals which are directed to the one or more panels <b>20</b>, as well as for reading signals sensed by the polarization antennas <b>26</b> of the panels <b>20</b> and for decoding the signals into an electronic radar output indicative of weather information, target detection and/or recognition in military and/or civilian applications. The coordinate system <b>110</b> includes a z direction along an axis <b>112</b> of the cylinder <b>102</b>. One of the polarization antennas <b>26</b> shown located at mn: m<sup>th </sup>row, n<sup>th </sup>column, is comprised of dipoles <b>28</b><i>a </i>and <b>28</b><i>b </i>with one of the dipoles shown by the notation “h” in <figref idref="DRAWINGS">FIG. 6</figref>, and the other dipole shown by the notation “v”. The dipoles h and v are located at φ<sub>n</sub>,z<sub>m </sub>on the surface <b>100</b>
0039<maths id="MATH-US-00001" num="00001"><math overflow="scroll"><mrow><msub><mover><mi>r</mi><mi>r</mi></mover><mi>mn</mi></msub><mo>=</mo><mrow><mrow><msub><mi>a</mi><mi>x</mi></msub><mo></mo><mi>R</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>ϕ</mi><mi>n</mi></msub></mrow><mo>+</mo><mrow><msub><mi>a</mi><mi>y</mi></msub><mo></mo><mi>R</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>ϕ</mi><mi>n</mi></msub></mrow><mo>+</mo><mrow><msub><mi>a</mi><mi>z</mi></msub><mo></mo><msub><mi>z</mi><mi>m</mi></msub></mrow></mrow></mrow></math></maths><br /> where R is a radius of the cylinder <b>102</b>, the row height z<sub>m</sub>, ranges from −D/2 to +D/2 where D is the axial length of the cylindrical array (equal to the diameter D of the WSR-88D), and the bold unit vectors represent the Cartesian coordinates. Azimuth location φ<sub>n </sub>is measured relative to an x axis and is φ<sub>n</sub>=nΔφ, n=1, 2, 3 . . . . The electric field at
0040<maths id="MATH-US-00002" num="00002"><math overflow="scroll"><mrow><mrow><mover><mi>r</mi><mi>r</mi></mover><mo>=</mo><mrow><mrow><msub><mi>a</mi><mi>x</mi></msub><mo></mo><mi>r</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ϕ</mi></mrow><mo>+</mo><mrow><msub><mi>a</mi><mi>y</mi></msub><mo></mo><mi>r</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ϕ</mi></mrow><mo>+</mo><mrow><msub><mi>a</mi><mi>z</mi></msub><mo></mo><mi>r</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi></mrow></mrow></mrow><mo>,</mo></mrow></math></maths><br /> transmitted by the mn<sup>th </sup>q (i.e., q=h or v) dipole, is (Ishimaru 1997, Section 2.4)
0041<maths id="MATH-US-00003" num="00003"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><mrow><msubsup><mover><mi>E</mi><mi>r</mi></mover><mi>mn</mi><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></msubsup><mo></mo><mrow><mo>(</mo><mover><mi>r</mi><mi>r</mi></mover><mo>)</mo></mrow></mrow><mo>=</mo><mrow><mrow><mo>-</mo><mfrac><mrow><msup><mi>k</mi><mn>2</mn></msup><mo></mo><msup><mi>e</mi><mrow><mrow><mo>-</mo><mi>j</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>k</mi><mo></mo><mrow><mo></mo><mrow><mover><mi>r</mi><mi>r</mi></mover><mo>-</mo><msub><mover><mi>r</mi><mi>r</mi></mover><mi>mn</mi></msub></mrow><mo></mo></mrow></mrow></msup></mrow><mrow><mn>4</mn><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>π</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ɛ</mi><mo></mo><mrow><mo></mo><mrow><mover><mi>r</mi><mi>r</mi></mover><mo>-</mo><msub><mover><mi>r</mi><mi>r</mi></mover><mi>mn</mi></msub></mrow><mo></mo></mrow></mrow></mfrac></mrow><mo></mo><mrow><msubsup><mover><mi>M</mi><mi>r</mi></mover><mi>mn</mi><mrow><mi>′</mi><mo></mo><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></mrow></msubsup><mo></mo><mrow><mo>(</mo><mrow><mi>θ</mi><mo>,</mo><mi>ϕ</mi></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mo>(</mo><mrow><mn>1</mn><mo></mo><mi>a</mi></mrow><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><br /> where k=2π/λ, λ is the radar wavelength, ε is the permittivity for an assumed uniform precipitation-free atmosphere,
0042<maths id="MATH-US-00004" num="00004"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><msubsup><mover><mi>M</mi><mi>I</mi></mover><mi>mn</mi><mrow><mi>′</mi><mo></mo><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></mrow></msubsup><mo></mo><mrow><mo>(</mo><mrow><mi>θ</mi><mo>,</mo><mi>ϕ</mi></mrow><mo>)</mo></mrow></mrow><mo>=</mo><mrow><msub><mi>a</mi><mi>r</mi></msub><mo>×</mo><mrow><mrow><mo>[</mo><mrow><msub><mi>a</mi><mi>r</mi></msub><mo>×</mo><msubsup><mover><mi>M</mi><mi>I</mi></mover><mi>mn</mi><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></msubsup></mrow><mo>]</mo></mrow><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo>[</mo><mrow><mi>Coulomb</mi><mo></mo><mstyle><mtext>-</mtext></mstyle><mo></mo><mi>meter</mi></mrow><mo>]</mo></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mrow><mn>1</mn><mo></mo><mi>b</mi></mrow><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><br /> where {right arrow over (M)}<sub>mn</sub><sup>(q) </sup>is the moment of dipole q at location mn, and a<sub>r </sub>is the unit vector along {right arrow over (r)}.
0043Using the far-field approximation, we have the electric field at {right arrow over (r)} radiated by the mn<sup>th </sup>q dipole
0044<maths id="MATH-US-00005" num="00005"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><msubsup><mover><mi>E</mi><mi>r</mi></mover><mi>mn</mi><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></msubsup><mo>=</mo><mrow><mrow><mo>[</mo><mtable><mtr><mtd><msubsup><mi>E</mi><mi>mn</mi><mrow><mo>(</mo><mi>h</mi><mo>)</mo></mrow></msubsup></mtd></mtr><mtr><mtd><msubsup><mi>E</mi><mi>mn</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></msubsup></mtd></mtr></mtable><mo>]</mo></mrow><mo>≈</mo><mrow><mi>A</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><msup><mi>e</mi><mrow><mi>jk</mi><mo></mo><mrow><mo>[</mo><mrow><mrow><msub><mi>z</mi><mi>m</mi></msub><mo></mo><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi></mrow><mo>+</mo><mrow><mi>R</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo>-</mo><msub><mi>ϕ</mi><mi>n</mi></msub></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo>]</mo></mrow></mrow></msup><mo></mo><mrow><mo>[</mo><mtable><mtr><mtd><msubsup><mi>M</mi><mi>mn</mi><mrow><mi>′</mi><mo></mo><mrow><mo>(</mo><mi>h</mi><mo>)</mo></mrow></mrow></msubsup></mtd></mtr><mtr><mtd><msubsup><mi>M</mi><mi>mn</mi><mrow><mi>′</mi><mo></mo><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></msubsup></mtd></mtr></mtable><mo>]</mo></mrow></mrow></mrow></mrow></mrow><mo></mo><mstyle><mtext></mtext></mstyle><mo></mo><mi>where</mi></mrow></mtd><mtd><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mi>a</mi></mrow><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mrow><mi>A</mi><mo>≡</mo><mrow><mo>-</mo><mrow><mfrac><mrow><msup><mi>k</mi><mn>2</mn></msup><mo></mo><msup><mi>e</mi><mrow><mrow><mo>-</mo><mi>j</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>kr</mi></mrow></msup></mrow><mrow><mn>4</mn><mo></mo><mi>πɛ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>r</mi></mrow></mfrac><mo>.</mo></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mrow><mn>2</mn><mo></mo><mi>b</mi></mrow><mo>)</mo></mrow></mtd></mtr></mtable></math></maths>
0045The superscript (h) is used to identify the dipole <b>28</b><i>a </i>(which extends in a horizontal direction as shown in <figref idref="DRAWINGS">FIG. 4</figref>), and the superscript (v) is used to identify the dipole <b>28</b><i>b </i>(which extends in a vertical direction as shown in <figref idref="DRAWINGS">FIG. 4</figref>). Following the procedure of Zhang et al., (2009a), the electric fields can be expressed in the plane of polarization (Doviak and Zrnic, 2006, <figref idref="DRAWINGS">FIG. 8.15</figref>) at {right arrow over (r)} as
0046<maths id="MATH-US-00006" num="00006"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><msubsup><mover><mi>E</mi><mi>I</mi></mover><mi>mn</mi><mrow><mo>(</mo><mi>h</mi><mo>)</mo></mrow></msubsup><mo>=</mo><mrow><msubsup><mi>E</mi><mi>imn</mi><mrow><mo>(</mo><mi>h</mi><mo>)</mo></mrow></msubsup><mo></mo><msubsup><mover><mi>e</mi><mi>r</mi></mover><mi>n</mi><mrow><mo>(</mo><mi>h</mi><mo>)</mo></mrow></msubsup></mrow></mrow><mo>,</mo><mrow><mrow><mi>and</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><msubsup><mover><mi>E</mi><mi>I</mi></mover><mi>mn</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></msubsup></mrow><mo>=</mo><mrow><msubsup><mi>E</mi><mi>imn</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></msubsup><mo></mo><msup><mover><mi>e</mi><mi>r</mi></mover><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></msup></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mrow><mrow><mn>3</mn><mo></mo><mi>a</mi></mrow><mo>,</mo><mi>b</mi></mrow><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><br /> where E<sub>t mn</sub><sup>(h) </sup>and E<sub>t mn</sub><sup>(v) </sup>are the fields respectively transmitted by the h and v dipoles along the normal to the plane of the dipoles (i.e., the crossed dipole's broadside direction) located at, φ<sub>n</sub>,z<sub>m</sub>. <br /> Thus, <br /><i>E</i><sub>t mn</sub><sup>(h)</sup><i>Ae</i><sup>jk[z</sup><sup><sub2>m</sub2></sup><sup>cos θ+R sin θ cos(φ−φ</sup><sup><sub2>n</sub2></sup><sup>)]</sup><i>M</i><sub>mn</sub><sup>(h)</sup>, (3c)<br /> with a like expression for E<sub>t mn</sub><sup>(v)</sup>, and {right arrow over (e)}<sub>n</sub><sup>(h) </sup>is
0047<maths id="MATH-US-00007" num="00007"><math overflow="scroll"><mtable><mtr><mtd><mrow><msubsup><mover><mi>e</mi><mi>r</mi></mover><mi>n</mi><mrow><mo>(</mo><mi>h</mi><mo>)</mo></mrow></msubsup><mo>=</mo><mrow><msub><mi>a</mi><msup><mi>y</mi><mi>′</mi></msup></msub><mo>-</mo><mrow><mo>[</mo><mstyle><mspace width="0.em" height="0.ex" /></mstyle><mo></mo><mrow><mrow><mrow><msub><mi>a</mi><msup><mi>x</mi><mi>′</mi></msup></msub><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo>-</mo><msub><mi>ϕ</mi><mi>n</mi></msub></mrow><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><mrow><mo> </mo><mrow><mrow><msub><mi>a</mi><msup><mi>y</mi><mi>′</mi></msup></msub><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo>-</mo><msub><mi>ϕ</mi><mi>n</mi></msub></mrow><mo>)</mo></mrow></mrow></mrow><mo>+</mo><mrow><msub><mi>a</mi><mi>z</mi></msub><mo></mo><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi></mrow></mrow><mo>]</mo></mrow><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo>-</mo><msub><mi>ϕ</mi><mi>n</mi></msub></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo>,</mo></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mrow><mn>3</mn><mo></mo><mi>d</mi></mrow><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><br /> a form analogous to Eq. (5a) of Zhang et al. (2009a), but one that accounts for the φ<sub>n </sub>angular rotation about z of the coordinate x, y axes, to x′, y′ for mn<sup>th </sup>element. {right arrow over (e)}<sup>(v) </sup>is
0048<maths id="MATH-US-00008" num="00008"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><msup><mover><mi>e</mi><mi>r</mi></mover><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></msup><mo>=</mo><mrow><mrow><msub><mi>a</mi><mi>z</mi></msub><mo></mo><msup><mi>sin</mi><mn>2</mn></msup><mo></mo><mi>θ</mi></mrow><mo>-</mo><mrow><mrow><mo>[</mo><mrow><mrow><msub><mi>a</mi><msup><mi>x</mi><mi>′</mi></msup></msub><mo></mo><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ϕ</mi></mrow><mo>+</mo><mrow><msub><mi>a</mi><msup><mi>y</mi><mi>′</mi></msup></msub><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>ϕ</mi></mrow></mrow><mo>]</mo></mrow><mo></mo><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi></mrow></mrow></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mo>(</mo><mrow><mn>3</mn><mo></mo><mi>e</mi></mrow><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><br /> which is identical to that given by Eq. (5b) of Zhang et al., (2009a). Note that {right arrow over (e)}<sub>n</sub><sup>(h) </sup>is a function of dipole location but {right arrow over (e)}<sup>(v) </sup>is not, and, as pointed out by Zhang et al. (2009a), {right arrow over (e)}<sup>(h) </sup>is not orthogonal to {right arrow over (e)}<sup>(v)</sup>.
0049To form a beam pointing in the (θ<sub>0</sub>,φ<sub>0</sub>) direction, a phase shift <br />Ψ<sub>mn</sub><i>=−k[z</i><sub>m </sub>cos θ<sub>0</sub><i>+R </i>sin θ<sub>0 </sub>cos(φ<sub>0</sub>−φ<sub>n</sub>)] (4)<br /> is applied to each of the mn polarization antenna element <b>26</b> that are used to form the beam <b>50</b>. The phase shifts given by (4) produce the beam <b>50</b> in the (θ<sub>0</sub>,φ<sub>0</sub>) direction.
0050The incident horizontal and so-called “vertical” (i.e., the vertical field lies in the vertical plane, but is only vertical at the 90° zenith angle) fields E<sub>ihmn </sub>and E<sub>ivmn </sub>in the plane of polarization are given by (Zhang et al., 2009a)
0051<maths id="MATH-US-00009" num="00009"><math overflow="scroll"><mtable><mtr><mtd><mrow><mstyle><mspace width="4.4em" height="4.4ex" /></mstyle><mo></mo><mrow><mrow><mrow><mo>[</mo><mtable><mtr><mtd><msub><mi>E</mi><mi>ihmn</mi></msub></mtd></mtr><mtr><mtd><msub><mi>E</mi><mi>ivmn</mi></msub></mtd></mtr></mtable><mo>]</mo></mrow><mo>=</mo><mrow><mrow><msub><mi>AP</mi><mi>mn</mi></msub><mo></mo><mrow><mo>[</mo><mtable><mtr><mtd><mrow><mo></mo><msubsup><mi>M</mi><mi>mn</mi><mrow><mo>(</mo><mi>h</mi><mo>)</mo></mrow></msubsup><mo></mo></mrow></mtd></mtr><mtr><mtd><mrow><mo></mo><msubsup><mi>M</mi><mi>mn</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></msubsup><mo></mo></mrow></mtd></mtr></mtable><mo>]</mo></mrow></mrow><mo></mo><mrow><mi>exp</mi><mo></mo><mrow><mo>(</mo><mrow><mi>j</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msubsup><mi>ψ</mi><mi>mn</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msubsup></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo></mo><mstyle><mtext></mtext></mstyle><mo></mo><mstyle><mspace width="1.1em" height="1.1ex" /></mstyle><mo></mo><mi>where</mi><mo></mo><mstyle><mtext></mtext></mstyle><mo></mo><mrow><mrow><msubsup><mi>ψ</mi><mi>mn</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msubsup><mo>=</mo><mrow><mi>k</mi><mo></mo><mrow><mo>{</mo><mrow><mrow><msub><mi>z</mi><mi>m</mi></msub><mo></mo><mrow><mo>[</mo><mrow><mrow><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi></mrow><mo>-</mo><mrow><mi>cos</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>θ</mi><mn>0</mn></msub></mrow></mrow><mo>]</mo></mrow></mrow><mo>+</mo><mrow><mi>R</mi><mo></mo><mrow><mo>[</mo><mrow><mrow><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo>-</mo><msub><mi>ϕ</mi><mi>n</mi></msub></mrow><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>θ</mi><mn>0</mn></msub><mo></mo><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><msub><mi>ϕ</mi><mn>0</mn></msub><mo>-</mo><msub><mi>ϕ</mi><mi>n</mi></msub></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo>]</mo></mrow></mrow></mrow><mo>}</mo></mrow></mrow></mrow><mo>,</mo><mstyle><mtext></mtext></mstyle><mo></mo><mstyle><mspace width="1.1em" height="1.1ex" /></mstyle><mo></mo><mi>and</mi></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mrow><mn>5</mn><mo></mo><mi>a</mi></mrow><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mrow><mstyle><mspace width="4.4em" height="4.4ex" /></mstyle><mo></mo><mrow><msub><mi>P</mi><mi>mn</mi></msub><mo>=</mo><mrow><mo>⌈</mo><mtable><mtr><mtd><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo>-</mo><msub><mi>ϕ</mi><mi>n</mi></msub></mrow><mo>)</mo></mrow></mrow></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mrow><mrow><mo>-</mo><mi>cos</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><mi>sin</mi><mo></mo><mrow><mo>(</mo><mrow><mi>ϕ</mi><mo>-</mo><msub><mi>ϕ</mi><mi>n</mi></msub></mrow><mo>)</mo></mrow></mrow></mrow></mtd><mtd><mrow><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>θ</mi></mrow></mtd></mtr></mtable><mo>⌉</mo></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mrow><mn>5</mn><mo></mo><mi>b</mi></mrow><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><br /> is a matrix that projects the polarization antenna element <b>26</b>'s broadside electric field to the plane of polarization at {right arrow over (r)}, and accounts for h dipole orientation at φ<sub>n</sub>. In this analysis we assume that each dipole <b>26</b><i>a </i>and <b>26</b><i>b </i>radiates only into the outward hemisphere having an equator in the plane of the crossed dipole <b>26</b><i>a </i>and <b>26</b><i>b</i>. Magnitude signs are placed around the dipole moment to emphasize that the dipole phase is incorporated into Ψ<sub>mn</sub><sup>(0)</sup>. Although the subscript index ‘m’ does not appear in the matrix, it is attached to P<sub>mn </sub>to emphasize that the projection applies to the mn<sup>th </sup>h and v dipoles. The subscript ‘h’ and ‘v’ on E<sub>ihmn </sub>and E<sub>ivmn </sub>denotes these are the horizontal and “vertical” fields transmitted by the mn<sup>th </sup>dipoles and incident on the scatterer; note E<sub>ivmn </sub>has contributions from both the h and v dipole moments, whereas E<sub>ihmn </sub>depends only on the h dipole's moment.
0052Radiation patterns with specified sidelobe levels and beamwidths can be achieved with a proper weight (w<sub>mn</sub><sup>(q)</sup>) applied to each polarization antenna element <b>26</b>. Hence, the total incident field at {right arrow over (r)} is the weighted contributions from all the active polarization antennas <b>26</b> used to form the beam <b>50</b> at (θ<sub>0</sub>,φ<sub>0</sub>). This field can be expressed as
0053<maths id="MATH-US-00010" num="00010"><math overflow="scroll"><mtable><mtr><mtd><mrow><mover><msub><mi>E</mi><mi>i</mi></msub><mi>r</mi></mover><mo>=</mo><mrow><mrow><mo>[</mo><mtable><mtr><mtd><msub><mi>E</mi><mi>ih</mi></msub></mtd></mtr><mtr><mtd><msub><mi>E</mi><mi>iv</mi></msub></mtd></mtr></mtable><mo>]</mo></mrow><mo>=</mo><mrow><mi>A</mi><mo></mo><mrow><munder><mo>∑</mo><mrow><mi>m</mi><mo>,</mo><mi>n</mi></mrow></munder><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><msub><mi>P</mi><mi>mn</mi></msub><mo></mo><mrow><msub><mi>W</mi><mi>mn</mi></msub><mo></mo><mrow><mo>[</mo><mtable><mtr><mtd><mrow><mo></mo><msup><mi>M</mi><mrow><mo>(</mo><mi>h</mi><mo>)</mo></mrow></msup><mo></mo></mrow></mtd></mtr><mtr><mtd><mrow><mo></mo><msup><mi>M</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></msup><mo></mo></mrow></mtd></mtr></mtable><mo>]</mo></mrow></mrow><mo></mo><mrow><mi>exp</mi><mo></mo><mrow><mo>(</mo><mrow><mi>j</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msubsup><mi>ψ</mi><mi>mn</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></msubsup></mrow><mo>)</mo></mrow></mrow></mrow></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><br /> where the weighting matrix W<sub>mn </sub>is applied to each polarization antenna element <b>26</b> used to form the beam <b>50</b>, and the angular dependence of the broadside field generated by the mn<sup>th </sup>h and v dipole moments is incorporated into W<sub>mn</sub>; that is all dipoles <b>26</b><i>a </i>and <b>26</b><i>b </i>have M<sup>(h)</sup>=M<sup>(v) </sup>which is taken to be the dipole's source excitation modulated by W<sub>mn</sub>. E<sub>ih </sub>is the total horizontal field generated by all the h and v dipoles that are used to form the beam <b>50</b>. Because the h dipoles change orientation depending on their azimuth φ<sub>n</sub>, the weighting vector can be expressed as
0054<maths id="MATH-US-00011" num="00011"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><msub><mi>W</mi><mi>mn</mi></msub><mo>=</mo><mrow><mrow><mo>[</mo><mtable><mtr><mtd><mfrac><mn>1</mn><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><msub><mi>ϕ</mi><mn>0</mn></msub><mo>-</mo><msub><mi>ϕ</mi><mi>n</mi></msub></mrow><mo>)</mo></mrow></mrow></mfrac></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mfrac><mn>1</mn><mrow><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>θ</mi><mn>0</mn></msub></mrow></mfrac></mtd></mtr></mtable><mo>]</mo></mrow><mo></mo><msubsup><mi>w</mi><mi>mn</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msubsup></mrow></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mo>(</mo><mrow><mn>7</mn><mo></mo><mi>a</mi></mrow><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><br /> where the upper-left matrix element
0055<maths id="MATH-US-00012" num="00012"><math overflow="scroll"><mfrac><mn>1</mn><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><msub><mi>ϕ</mi><mn>0</mn></msub><mo>-</mo><msub><mi>ϕ</mi><mi>n</mi></msub></mrow><mo>)</mo></mrow></mrow></mfrac></math></maths><br /> compensates for the projection loss of the H-dipole radiated field onto the horizontal polarization direction along the boresight of the beam <b>50</b>. In a preferred embodiment, the boresight always lies in the plane containing the bisector of the angle encompassing the azimuth sector containing the dipoles <b>26</b><i>a </i>and <b>26</b><i>b </i>forming the beam <b>50</b>; in effect the boresight of the cylindrical configuration for the polarimetric phased array antenna <b>12</b> is always in the broadside direction. Alternatively <br />φ<sub>n</sub><i>=nΔφ=φ</i><sub>0</sub><i>±n′Δφ=</i>(<i>n</i><sub>0</sub><i>±n</i>′)Δφ,[<i>n′=</i>0,1,2, . . . <i>N</i><sub>a</sub>], (7b)<br /> is the location of the active dipoles <b>26</b><i>a </i>and <b>26</b><i>b </i>in an angular sector (e.g., 120° for a 3 beam CPPAR) centered on φ<sub>0 </sub>with (2N<sub>a</sub>+1) active array elements in the azimuthal span of [n<sub>0</sub>−N<sub>a</sub>, n<sub>0</sub>+N<sub>a</sub>]. Likewise, the lower-right matrix element
0056<maths id="MATH-US-00013" num="00013"><math overflow="scroll"><mfrac><mn>1</mn><mrow><mi>sin</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>θ</mi><mn>0</mn></msub></mrow></mfrac></math></maths><br /> compensates for the projection loss of the V-dipole radiated field onto the vertical direction; this correction is normally close to unity because the elevation angle (π/2−θ<sub>0</sub>) for weather measurements is typically small.
0057The scalar weight w<sub>mn</sub><sup>(i) </sup>is for isotropic radiators; these weights are selected to control the sidelobe levels. The WSR-88D antenna pattern is mimicked by selecting
0058<maths id="MATH-US-00014" num="00014"><math overflow="scroll"><mtable><mtr><mtd><mrow><msubsup><mi>w</mi><mi>mn</mi><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></msubsup><mo>=</mo><mrow><mrow><mo>(</mo><mfrac><mrow><mrow><mo>{</mo><mrow><mn>1</mn><mo>-</mo><mrow><mrow><mn>4</mn><mo></mo><mrow><mo>[</mo><mrow><mrow><msup><mi>R</mi><mn>2</mn></msup><mo></mo><mrow><msup><mi>sin</mi><mn>2</mn></msup><mo></mo><mrow><mo>(</mo><mrow><msub><mi>ϕ</mi><mn>0</mn></msub><mo>-</mo><msub><mi>ϕ</mi><mi>n</mi></msub></mrow><mo>)</mo></mrow></mrow></mrow><mo>+</mo><msubsup><mi>z</mi><mi>m</mi><mn>2</mn></msubsup></mrow><mo>]</mo></mrow></mrow><mo>/</mo><msup><mi>D</mi><mn>2</mn></msup></mrow></mrow><mo>}</mo></mrow><mo>+</mo><mi>b</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>b</mi></mrow></mfrac><mo>)</mo></mrow><mo></mo><mrow><mrow><mi>cos</mi><mo></mo><mrow><mo>(</mo><mrow><msub><mi>ϕ</mi><mn>0</mn></msub><mo>-</mo><msub><mi>ϕ</mi><mi>n</mi></msub></mrow><mo>)</mo></mrow></mrow><mo>.</mo></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>8</mn><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><br /> The term in the parenthesis is equivalent to the WSR-88D illumination taper but applied to those mn<sup>th </sup>dipoles whose projection onto the vertical plane bisecting the cylinder lies within the πD<sup>2</sup>/4 area where D is the diameter of the WSR-88D dish antenna (dipoles outside this circular area, but lying within the angular sector of elements forming the beam <b>50</b>, have zero weight); the cos(φ−φ<sub>0</sub>) term accounts for the change of the density of the array elements projected onto the vertical plane and the term b=0.16 accounts for edge illumination of the WSR-88D reflector (Doviak et al., 1998). Although w<sub>mn</sub><sup>(i) </sup>mimics the illumination taper on the WSR-88D antenna for the boresight direction, the analogy no longer exists for azimuths in off-boresight directions. This is because the polarization antennas <b>26</b> that are active on the cylinder <b>102</b> have a density that lacks the symmetry of the dish antenna about the vertical bisector of the circular area.
0059On the beam's boresight (i.e., 0=θ=θ<sub>0</sub>, φ=φ<sub>0</sub>), the radiated fields from all the polarization antennas <b>26</b> are in phase so the phase term in (6) disappears and the incident wave field becomes
0060<maths id="MATH-US-00015" num="00015"><math overflow="scroll"><mtable><mtr><mtd><mrow><mover><msub><mi>E</mi><mi>i</mi></msub><mi>r</mi></mover><mo>=</mo><mrow><mi>A</mi><mo></mo><mrow><munder><mo>∑</mo><mrow><mi>m</mi><mo>,</mo><mi>n</mi></mrow></munder><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><msub><mi>P</mi><mi>mn</mi></msub><mo></mo><msub><mi>W</mi><mi>mn</mi></msub><mo></mo><mrow><mrow><mo></mo><msup><mover><mi>M</mi><mi>r</mi></mover><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></msup><mo></mo></mrow><mo>.</mo></mrow></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><br /> Because the polarization antennas <b>26</b> that are active and the weighting factor w<sub>mn</sub><sup>(i) </sup>are symmetric about φ<sub>0 </sub>and z<sub>m</sub>=0, there is no on-axis cross-polar radiation. That is, within a sector, the vertically polarized wave field caused by the horizontal dipole <b>28</b><i>a </i>at φ<sub>0</sub>−n′Δφ cancels that field from the horizontal dipole <b>28</b><i>a </i>at the opposite azimuth φ<sub>0</sub>+n′Δφ. This cross-polar null on-axis is important for accurate polarimetric radar measurement of precipitation (Wang and Chandrasekar 2006; Zrnic et al. 2010). This is one of the main reasons for using the cylindrical configuration for the polarimetric phased array antenna <b>12</b> commutating scan in which the beam direction changes in azimuth by shifting a column of active polarization antennas <b>26</b>, and maintaining the weights symmetry about the beam center. This way, the beam characteristics of the cylindrical configuration for the polarimetric phased array antenna <b>12</b> are scan invariant; not so for the planar polarimetric phased array radar discussed in the Background section.
0061Given the field incident on a hydrometer, the scattered wave field can be expressed as [Doviak and Zrnić 2006, Section 8.5.2.1]
0062<maths id="MATH-US-00016" num="00016"><math overflow="scroll"><mtable><mtr><mtd><mrow><mrow><msub><mover><mi>E</mi><mi>r</mi></mover><mi>s</mi></msub><mo>=</mo><mrow><mrow><mo>[</mo><mtable><mtr><mtd><msub><mi>E</mi><mi>sh</mi></msub></mtd></mtr><mtr><mtd><msub><mi>E</mi><mi>sv</mi></msub></mtd></mtr></mtable><mo>]</mo></mrow><mo>=</mo><mrow><msup><mi>S</mi><mi>′</mi></msup><mo></mo><msub><mover><mi>E</mi><mi>r</mi></mover><mi>i</mi></msub><mo>×</mo><mfrac><mrow><mi>exp</mi><mo></mo><mrow><mo>(</mo><mrow><mrow><mo>-</mo><mi>j</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>kr</mi></mrow><mo>)</mo></mrow></mrow><mi>r</mi></mfrac></mrow></mrow></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mo>(</mo><mn>10</mn><mo>)</mo></mrow></mtd></mtr></mtable></math></maths><br /> where S′ is the backscatter matrix of a hydrometeor and includes propagation effects (Zhang et al. 2009a).
0063Although (10) can give the H, V electric fields at any receiving polarization antenna element <b>26</b> in the array, the fields parallel to the respective dipole axis should be determined. The fields parallel to the dipole axes are obtained by projecting {right arrow over (E)}<sub>s mn </sub>onto the respective dipole directions, and with the proper weighting and phase shifts. In this case the total received wave field is expressed as
0064<maths id="MATH-US-00017" num="00017"><math overflow="scroll"><mtable><mtr><mtd><mrow><msub><mover><mi>E</mi><mi>r</mi></mover><mi>r</mi></msub><mo>=</mo><mrow><mrow><munder><mo>∑</mo><mrow><mi>m</mi><mo>,</mo><mi>n</mi></mrow></munder><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><msub><mi>W</mi><mi>mn</mi></msub><mo></mo><msubsup><mi>P</mi><mi>mn</mi><mi>t</mi></msubsup><mo></mo><msub><mover><mi>E</mi><mi>r</mi></mover><mi>smn</mi></msub><mo></mo><msup><mi>e</mi><mrow><mrow><mo>-</mo><mi>j</mi></mrow><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mi>ψ</mi><mi>mn</mi></msub></mrow></msup></mrow></mrow><mo>=</mo><mrow><munder><mo>∑</mo><mrow><mi>m</mi><mo>,</mo><mi>n</mi></mrow></munder><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mrow><msubsup><mi>W</mi><mi>mn</mi><mi>t</mi></msubsup><mo></mo><msubsup><mi>P</mi><mi>mn</mi><mi>t</mi></msubsup><mo></mo><msup><mi>S</mi><mi>′</mi></msup><mo></mo><msub><mi>P</mi><mi>mn</mi></msub><mo></mo><msub><mi>W</mi><mi>mn</mi></msub><mo></mo><msup><mover><mi>M</mi><mi>r</mi></mover><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></msup><mo>×</mo><mrow><mo>(</mo><mrow><mo>-</mo><mfrac><msup><mi>k</mi><mn>2</mn></msup><mrow><mn>4</mn><mo></mo><mi>πɛ</mi></mrow></mfrac></mrow><mo>)</mo></mrow><mo></mo><mrow><mfrac><mrow><mi>exp</mi><mo></mo><mrow><mo>(</mo><mrow><mrow><mo>-</mo><mn>2</mn></mrow><mo></mo><mi>j</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mi>kr</mi></mrow><mo>)</mo></mrow></mrow><msup><mi>r</mi><mn>2</mn></msup></mfrac><mo>.</mo></mrow></mrow></mrow></mrow></mrow></mtd><mtd><mrow><mo>(</mo><mn>11</mn><mo>)</mo></mrow></mtd></mtr></mtable></math></maths>
0065The operational WSR-88D radar has high performance for meteorological observations: it has a dish antenna with a diameter of 8.54 m, a beam width of about 1 degree, and the first sidelobe below −26 dB. It is desirable for the cylindrical configuration for the polarimetric phased array antenna <b>12</b> to have similar or better performance. <figref idref="DRAWINGS">FIG. 7</figref> shows a table of the specifics of sample designs for the cylindrical configuration for the polarimetric phased array antenna <b>12</b> with two, three, or four beams <b>50</b>; each mimics the NEXRAD beamwidth at the largest electronic scan angle, and element separations used are 1.0, 0.75 and 0.5 wavelength. Considering the tradeoff for maximizing the effective aperture and the number of beams <b>50</b>, it is efficient to use either three or four simultaneous beams <b>50</b> for the cylindrical configuration for the polarimetric phased array antenna <b>12</b> consistent with what is recommended by Josefsson and Persson (2006, Chapter 3). It is relatively easy to control sidelobes with the four beams <b>50</b> and short distance for polarization antenna element <b>26</b> separations. For comparison, a planar polarimetric phased array antenna of three- and four-faces having a beamwidth, at its largest scanning azimuth angle (60°/45°), to match the WSR-88D is also shown in the table of <figref idref="DRAWINGS">FIG. 7</figref>.
0066In the case of three beams <b>50</b>, a 120 degree sector of the cylindrical configuration for the polarimetric phased array antenna <b>12</b> is used to form the beam <b>50</b>. This would require a cylinder of 8.54/sin(60°)=9.88 m diameter and 8.54 m height. This is significantly smaller than the 17.1 m (i.e., 8.54×2) major axis of the elliptical array for a three-face planar polarimetric phased array antenna that matches, at the extremes of electronic steering of 60 degree, the WSR-88D resolution; furthermore there is no need to increase the total power by a factor of 16 (12 dB) to compensate for the loss of detection capability in these directions. For the four simultaneous beams, a 90 degree sector is used to form the beam <b>50</b>. The cylinder <b>102</b> of 12.1 m (˜8.54×√{square root over (2)}) diameter can be used. The diameter of the cylinder <b>102</b> is the same as the major axis of the elliptical array of the four-face planar polarimetric phased array antenna, and the total number of polarization antennas <b>26</b> for the cylindrical configuration for the polarimetric phased array antenna <b>12</b> is the same as for the planar polarimetric phased array antenna. A sector of polarization antennas <b>26</b> can have a rectangular shape for four corners. But, the polarization antennas <b>26</b> at the corners of the sector of the cylindrical configuration for the polarimetric phased array antenna <b>12</b> can be used for sidelobe blanking and pattern synthesis whereas the planar polarimetric phased array antenna would have to have extra elements for such functions. Also the total power of the cylindrical configuration for the polarimetric phased array antenna <b>12</b> does not need to be increased by a factor of four (6 dB). Assuming that the spacing between the polarization antennas <b>26</b> is the wavelength of 10 cm, there would be 380 array columns and a total of 32680 elements covering the cylinder <b>102</b>. Commutating one column, the cylindrical configuration for the polarimetric phased array antenna <b>12</b> beam moves 0.95°—about the beam width. If the spacing between the polarization antennas <b>26</b> is reduced to one half a wavelength (i.e., 5 cm), <b>760</b> array columns would be needed to cover the cylinder <b>102</b>; this significantly increases the number of total polarization antennas <b>26</b> to 130720. Nevertheless, this will allow over-sampling at a 0.474° angular spacing, and lower sidelobes. Such fine angular sampling can also be achieved with the one wavelength spacing of the polarization antennas <b>26</b>, but then the phase of each column would need to be shifted by half the angular increment between the polarization antennas <b>26</b>.
0067Shown in <figref idref="DRAWINGS">FIGS. 8, 9, 10 and 11</figref> are calculated one-way radiation patterns for the aforementioned four beam case of the cylindrical configuration for the polarimetric phased array antenna <b>12</b> and their comparisons with theoretical WSR-88D patterns. In particular, <figref idref="DRAWINGS">FIGS. 8(<i>a</i>) and 8(<i>b</i>)</figref> show 3D copolar and cross-polar patterns for an exemplary polarimetric phased array antenna <b>12</b> with tapering and polarization compensation. The cross-polar radiation is everywhere at least 45 dB below the copolar peak indicating the polarimetric phased array antenna <b>12</b> has high performance for preserving polarization purity. In <figref idref="DRAWINGS">FIGS. 9, 10, and 11</figref> are the copolar patterns on the two planes through the boresight: the patterns on the horizontal plane are shown in upper panels (a) and (b), and those on vertical plane are in lower panels (c) and (d).
0068<figref idref="DRAWINGS">FIG. 9</figref> shows the copolar patterns whereby the dipoles <b>28</b><i>a </i>and <b>28</b><i>b </i>do not have any equivalent tapering of the WSR-88D illumination, density adjustment, and polarization compensation. Because the WSR-88D pattern is for the tapered illumination, the simulated copular patterns for the polarimetric phased array antenna <b>12</b> has higher sidelobes in <figref idref="DRAWINGS">FIGS. 9(<i>a</i>) and (<i>c</i>)</figref>. This is also true for the near sidelobes as seen in the zoomed-in plots on the right in <figref idref="DRAWINGS">FIGS. 9(<i>b</i>) and (<i>d</i>)</figref>. The pattern sidelobes for horizontal polarization are a little lower than for vertical polarization because of the natural tapering caused by changes in orientation of the horizontal dipoles as a function of φ<sub>n</sub>.
0069<figref idref="DRAWINGS">FIG. 10</figref> shows a simulated copolar pattern if Eq. 8, without the cosine term, is applied to the dipoles <b>28</b><i>a </i>and <b>28</b><i>b </i>within the angular sector forming the beam <b>50</b>. The sidelobes are substantially reduced except near ±90 degree azimuth angles. This is due to a non-symmetrical density of the polarization antennas <b>26</b> that are active and seen from off-broadside directions. Nevertheless, the level is 50 dB below the copolar peak and for two-way patterns that are of interest for meteorological applications, the sidelobe level is 100 dB below the copolar peak. This low sidelobe level is due to the applied tapering. It is also noted that the difference between the two polarizations is now very small because the main contribution to the radiation field comes from polarization antennas <b>26</b> within the array near the broadside where there is not much difference in H- and V-polarizations. If density adjustment (i.e., the cosine term in Eq. 8) and polarization compensation are applied, the results become even better (<figref idref="DRAWINGS">FIG. 8</figref>). The main-lobes are almost identical to the WSR-88D reference pattern, which is crucial for high quality polarimetric radar measurements. Although sidelobes still exist, the farther sidelobes are mostly lower than those of WSR-88D's. This is because of the natural tapering in the polarimetric phased array antenna <b>12</b> having the cylindrical configuration.
0070In this patent application, the planar and cylinder array configuration of PPAR for weather measurements have been compared, and a theory for studying the cylindrical configuration of the polarimetric phased array antenna <b>12</b> has been proposed. Ideal array polarization antennas <b>26</b> have been assumed with given excitation. It is known that a planar polarimetric phased array radar has issues of scan-dependent beam properties including changes in beam and polarization characteristics, polarization coupling, sensitivity loss, and complications in calibration. To compensate for loss of sensitivity loss, the four-faced planar polarimetric phased array radar antenna would have to have a diagonal dimension doubling the size of the WSR-88D and an increase of power by a factor of 4.
0071The radar data acquisition system <b>10</b> having the polarimetric phased array antenna <b>12</b>, on the other hand, can also make azimuth scan-invariant, high accuracy weather measurements without changing the beam and polarization characteristics while maintaining a manageable antenna size. Compared with the planar polarimetric phased array radar, the preferred embodiment of the polarimetric phased array antenna <b>12</b> has the following advantages: <ul id="ul0001" list-style="none"><li id="ul0001-0001" num="0000"><ul id="ul0002" list-style="none"><li id="ul0002-0001" num="0072">1) Scan-invariant polarimetric radar measurements with the same beam width and polarization characteristics in all azimuth angles for each elevation, allowing easier calibration and data interpretation.</li><li id="ul0002-0002" num="0073">2) Polarization purity—dual-polarized (H and V) wave fields may be orthogonal in all direction, and hence maintains high quality polarimetric data. Compensation may only be needed for horizontal and vertical polarizations separately, but cross-polarization isolation may be maintained.</li><li id="ul0002-0003" num="0074">3) High efficiency of utilizing radiation power. Only certain polarization antennas <b>26</b> within the array are activated and properly weighted to achieve the desired beams <b>50</b>. The polarization antennas <b>26</b> on the broadside are mostly activated and weighted higher resulting in less scanning loss due to element radiation pattern.</li><li id="ul0002-0004" num="0075">4) Efficient use of spectrum. For example, the side-by-side and back-to-back beams <b>50</b> might use the same frequency because such beams <b>50</b> can be a fixed spacing such as 90 (120) degrees apart in the case of four (three) beams.</li><li id="ul0002-0005" num="0076">5) Optimal use of the antenna aperture for fast data update and/or for multi-functionality with more than one simultaneous beam <b>50</b>.</li><li id="ul0002-0006" num="0077">6) Flexibility to choose the number of beams <b>50</b> (e.g., two, three or four) and assign different tasks among beams <b>50</b>. For example, if four beams <b>50</b> are generated, two beams <b>50</b> can be used for weather surveillance and the other two beams <b>50</b> for aircraft tracking—making the radar data acquisition system <b>10</b> having the polarimetric phased array antenna <b>12</b> a multi-function phased array radar. This flexibility can be combined with multiple frequencies used in currently proposed planar polarimetric phased array radar, i.e., one band of frequencies for the weather function and another band for aircraft surveillance. The beams <b>50</b> can be created differently (size, shape . . . ) for different tasks (e.g. target tracking versus weather observation), and signals can be transmitted and interpreted differently (number of pulse, polarization mode, and signal processing . . . ). Further, different tasks may have different standards that need to be taken into account in signal transmission and processing.</li><li id="ul0002-0007" num="0078">7) No need for face-to-face matching as required for a planar polarimetric phased array radar where each face is an individual radar system having different characteristics that need to be matched with the other face(s).</li><li id="ul0002-0008" num="0079">8) If mounted on a rotatable support system <b>18</b>, the broadside patterns can be measured nad calibrated on site. <br /> References in the specification to “one embodiment”, “an embodiment”, “an example embodiment”, etc. indicate that the embodiments described may include a particular feature, structure or characteristic, but every embodiment may not necessarily include the particular feature, structure or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with an embodiment, it is submitted that it is within the knowledge of one skilled in the art to effect such future, structure, or characteristic in connection with other embodiments whether or not explicitly described. </li></ul></li></ul>
0080Embodiments of the invention with respect to the radar control and processing system <b>14</b> may be embodied utilizing machine executable instructions provided or stored on a machine readable medium. A machine-readable medium includes any mechanism which provides, that is, stores and/or transmits, information accessible by communication server, <b>34</b>, digital signal processor <b>36</b>, synchronizer <b>38</b>, RF source <b>40</b>, data acquisition unit <b>42</b>, the host computer <b>44</b>, and/or the user/maintenance workstation <b>46</b>. Each of the elements forming a part of the radar control and processing system <b>14</b> can include a set of one or more processors, etc. that work together. In an exemplary embodiment, a machine-readable medium includes volatile and/or non-volatile media for example read-only memory, random access memory, magnetic disk storage media, optical storage media, flash memory devices or the like.
0081Such machine executable instructions are utilized to cause a general or special purpose processor, multiple processors, or the like to perform methods or processes of the embodiments of the invention.
0082It should be understood that the components of the inventions set forth above can be provided as unitary elements, or multiple elements which are connected and/or otherwise adapted to function together, unless specifically limited to a unitary structure in the claims. For example, although the transmitter <b>30</b> is depicted as a unitary element, the transmitter <b>30</b> could be comprised of multiple discrete elements which are connected together using any suitable technology. As another example, the digital signal processor(s) <b>36</b> and the synchronizer(s) <b>38</b> may be implemented on a single computer system having one or more local bus and/or processors.
0083From the above description it is clear that the present invention is well adapted to carry out the disclosed aspects, and to attain the advantages mentioned herein as well as those inherent in the invention. While presently preferred implementations of the invention have been described for purposes of disclosure, it will be understood that numerous changes may be made which readily suggest themselves to those skilled in the art and which are accomplished within the spirit of the invention disclosed.
REFERENCES
0084The specific parts of the references referred to above are hereby incorporated herein by reference. <ul id="ul0003" list-style="none"><li id="ul0003-0001" num="0085">Brandes, E., G. Zhang, and J. Vivekanandan, 2003: An evaluation of a drop distribution-based rainfall estimator, <i>J. Appl. Meteor., </i>42(5), 652-660.</li><li id="ul0003-0002" num="0086">Brookner, E., 2008: Now: Phased-array Radars: Past, Astounding Breakthroughs and Future Trends, <i>Microwave Journal, </i>52(1), 1-30.</li><li id="ul0003-0003" num="0087">Doviak, R. J., D. S. Zrnić, J. Carter, A. Ryzhkov, S. Torres, and A. Zahrai, 1998: Polarimetric Upgrades to Improve Rainfall Measurements. Report of the National Severe Storms Laboratory, Norman, Okla., April, 110 pp.</li><li id="ul0003-0004" num="0088">Doviak, R. J., V. Bringi, A. Ryzhkov, A. Zahrai, and D. Zrnić, 2000: Considerations for polarimetric upgrades to operational WSR-88D radars,” <i>Journal of Atmospheric and Oceanic Technology, </i>17, 257-278.</li><li id="ul0003-0005" num="0089">Doviak and Zrnić, 2006: <i>Doppler Radar and Weather Observations, </i>2<sup>nd </sup>Edition, Academic Press, 1993; reprinted by Dover publications 562 pp.</li><li id="ul0003-0006" num="0090">Fulton, C., P. Clough, V. Pai, and W. Chappell, 2009: A digital array radar with a hierarchical system architecture,” IEEE MTT-S International Microwave Symposium Digest, June 2009, 89-92.</li><li id="ul0003-0007" num="0091">Heinselman, P. L., D. L. Priegnitz, K. L. Manross, T. M. Smith, and R. W. Adams, 2008: Rapid</li><li id="ul0003-0008" num="0092">sampling of severe storms by the National Weather Radar Testbed Phased Array Radar. Weather and Forecasting, 23, 808-824.</li><li id="ul0003-0009" num="0093">Hopf, A., J. L. Salazar, R. Medina, V. Venkatesh, E. J. Knapp, S. J. Frasier, and D. J. McLaughlin, 2009: Casa phased array radar system description, simulation and products. IEEE International Symposium on Geoscience and Remote Sensing, volume 4.</li><li id="ul0003-0010" num="0094">Ishimaru, A., 1997: <i>Wave propagation and scattering in random media</i>. IEEE Press, New York, N.Y., 574 pp.</li><li id="ul0003-0011" num="0095">K. Le, R. Palmer, B. Cheong, T. Yu, G. Zhang, and S. Tones, 2009: On the Use of Auxiliary Receive Channels for Clutter Mitigation on Phased Array Weather Radar, IEEE Transactions on Geoscience and Remote Sensing, 47, 272-284.</li><li id="ul0003-0012" num="0096">Office of Federal Coordinator for Meteorology, Multifunction Phased Array Radar Symposium II, http://www.ofcm.noaa.gov/mpar-symposium/, 17-19 November, 2009, Norman, Okla.</li><li id="ul0003-0013" num="0097">Raffaelli, S., and M. Johansson, 2003: Conformal array antenna demonstrator for WCDMA applications, Proceedings of Antenna 03, Kalmar, Sweden, 13-15 May 2003, pp. 207-212.</li><li id="ul0003-0014" num="0098">Royer, G. M., Directive gain and impedance of ring array of antennas, 1966: IEEE Trans. on Antennas and Propagation, 52, 1013-1021.</li><li id="ul0003-0015" num="0099">Sherman, S. M., 1988: Monopulse Principles and Techniques, Chapter 5 in <i>Aspects of Modern Radar</i>, E. Brookner, editor. Artech House, Boston, pp. 297-335.</li><li id="ul0003-0016" num="0100">Smith, P., J. Davis, E. Im, J. Lazo, D. McLaughlin, R. Palmer, S. Rutledge, S. Sandgathe, R. Serafin, M. Wolfson, and C. Marshall, 2008: <i>Evaluation of the Multifunction Phased Array Radar Planning Process, National Research Council Report</i>, August, 2008.</li><li id="ul0003-0017" num="0101">Tomasic, B., J. Turtle, and S. Liu, <i>A Geodesic Sphere Phased Array Antenna for Satellite Control and Communication, International Union of Radio Science, XXVIIth General Assembly</i>, Maastricht, The Netherlands, August 2002.</li><li id="ul0003-0018" num="0102">Wang, Y., and V. Chandrasekar, Polarization isolation requirements for linear dual-polarization weather radar in simultaneous transmission mode of operation, <i>IEEE Trans. Geosci. Remote Sensing, </i>40(8), 2019-2028, 2006.</li><li id="ul0003-0019" num="0103">Weber, M. E., J. Y. N. Cho, J. S. Herd, J. M. Flavin, W. E. Benner, and G. S. Torok, 2007: The next-generation multimission U.S. surveillance radar network. <i>Bull. Amer. Meteor. Soc., </i>88, 1739-1751.</li><li id="ul0003-0020" num="0104">Wurman, J., 2003: Preliminary results from the Rapid-DOW, a multi-beam inexpensive alternative to phased arrays, 31st Conference on Radar Meteorology, Seattle, American Meteorological Society</li><li id="ul0003-0021" num="0105">Yu, T., M. B. Orescanin, C. D. Curtis, D. S. Zrnic, and D. E. Forsyth, 2007: Beam multiplexing using the phased-array weather radar, <i>J. Atmos. Ocean. Tech, </i>24(4), 616-626.</li><li id="ul0003-0022" num="0106">Zhang, G., J. Vivekanandan, and E. Brandes, 2001: A method for estimating rain rate and drop size distribution form polarimetric radar measurements. <i>IEEE Trans. on Geoscience and Remote Sensing, </i>39(4), 831-841.</li><li id="ul0003-0023" num="0107">Zhang, G., and R. J. Doviak, 2007: Spaced antenna interferometry to measure crossbeam wind, shear, and turbulence: Theory and formulation, <i>J. Atmos. Ocean. Tech., </i>24(5), 791-805.</li><li id="ul0003-0024" num="0108">Zhang, G., and R. J. Doviak, 2008: Spaced antenna interferometry to detect and locate subvolume inhomogeneities of reflectivity: an analogy with monopulse radar, <i>J. Atmos. Ocean. Tech., </i>25(11), 1921-1938.</li><li id="ul0003-0025" num="0109">Zhang, G., R. J. Doviak, D. S. Zrnic, J. E. Crain, D. Staiman, and Y. Al-Rashid, 2009a: Phased array radar polarimetry for weather sensing: A theoretical formulation for polarization calibration. <i>IEEE Trans. on Geoscience and Remote Sensing, </i>47(11), 3679-3689.</li><li id="ul0003-0026" num="0110">Zhang, G., R. D. Palmer, D. S. Zrnic, and R. J. Doviak, 2009b: A cylindrical polarimetric phased array radar. U.S. Provisional patent application identified by U.S. Ser. No. 61/261,695.</li><li id="ul0003-0027" num="0111">Zhang, G., Y. Li, R. J. Doviak, D. Priegnitz, J. Carter, and C. Curtis, 2010: Multi-patterns of the National Weather Radar Testbed Mitigate Clutter Received via Sidelobes, <i>J. Atmos. Ocean. Tech</i>., Under review</li><li id="ul0003-0028" num="0112">Zrnić, D. S., J. F. Kimpel, D. E. Forsyth, A. Shapiro, G. Crain, R. Ferek, J. Heimmer, W.</li><li id="ul0003-0029" num="0113">Benner, T. J. McNellis, and R. J. Vogt, 2007: Agile-beam phased array radar for weather observations. <i>Bull. Amer. Meteor. Soc., </i>88(11)1753-1766.</li><li id="ul0003-0030" num="0114">Zrnic, D. S., R. J. Doviak, G. Zhang, and A. Ryzhkov, 2010: Bias in differential reflectivity due to cross coupling through the radiation patterns of polarimetric weather radars, <i>J. Atmos. Oceanic Tech</i>. Accepted.</li></ul>
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| Email NotificationEML_NTR | EML_NTR | |
| PG-Pub Issue NotificationPG-ISSUE | PG-ISSUE | |
| Patent Term Adjustment - Ready for ExaminationPTA.RFE | PTA.RFE | |
| Additional Application Filing FeesADDFLFEE | ADDFLFEE | |
| Electronic ReviewELC_RVW | ELC_RVW | |
| Email NotificationEML_NTR | EML_NTR | |
| Email NotificationEML_NTF | EML_NTF | |
| Filing ReceiptFLRCPT.O | FLRCPT.O | |
| Notice Mailed--Application Incomplete--Filing Date AssignedINCD | INCD | |
| Applicant Has Filed a Verified Statement of Small Entity Status in Compliance with 37 CFR 1.27SMAL | SMAL | |
| Cleared by OIPE CSRL194 | L194 | |
| Applicants have given acceptable permission for participating foreignAPPERMS | APPERMS | |
| IFW Scan & PACR Auto Security ReviewSCAN | SCAN | |
| Entity Status Set To Undiscounted (Initial Default Setting or Status Change)BIG. | BIG. | |
| Initial Exam Team nnIEXX | IEXX |
8 legal events, as the office reported them to INPADOC
Over the term
Point at a mark for the eventEvents
| Event | Code | |
|---|---|---|
| Lapsed due to failure to pay maintenance feeLapsedFP | FP | |
| Lapse for failure to pay maintenance feesLapsedPATENT EXPIRED FOR FAILURE TO PAY MAINTENANCE FEES (ORIGINAL EVENT CODE: EXP.); ENTITY STATUS OF PATENT OWNER: SMALL ENTITYLAPS | LAPS | |
| Information on status: patent discontinuationPATENT EXPIRED DUE TO NONPAYMENT OF MAINTENANCE FEES UNDER 37 CFR 1.362STCH | STCH | |
| Fee payment procedureMAINTENANCE FEE REMINDER MAILED (ORIGINAL EVENT CODE: REM.); ENTITY STATUS OF PATENT OWNER: SMALL ENTITYFEPP | FEPP | |
| Maintenance fee paymentMAFP | MAFP | |
| Certificate of correctionCC | CC | |
| Information on status: patent grantGrantedPATENTED CASESTCF | STCF | |
| AssignmentAS | AS |
Numbers
- Publication
- 09778357
- Publication, DOCDB
- 9778357
- Publication, EPODOC
- US9778357
- Application
- 14665813
- Application, DOCDB
- 201514665813
- Application, EPODOC
- US201514665813
Titles
- English
- Cylindrical polarimetric phased array radar
Patent term adjustment
- A delay
- +206 daysthe office missed an examination deadline
- Applicant delay
- −29 days
- Net adjustment
- 177 days
Classification
- CPC, 8
- G01S13/95
- G01S7/024
- H01Q3/24
- G01S2013/0272
- H01Q3/26
- H01Q21/205
- G01S2013/0245
- Y02A90/10
- IPC, 6
- G01S13 95
- G01S7 02
- H01Q3 26
- H01Q21 20
- H01Q3 24
- G01S13 02
- USPC, 1
- 001001000